The invention relates to a method for correcting optical wavefront errors according to the preamble of claim 1 and to a telescope having the general features of claims 3 and 5.
Optics are often concerned with point-like objects. The classical example is astronomy, where telescopes are used to register virtually point-like star images. Another, modern example is the optical linking of two satellites for the purpose of data exchange. Each satellite transmits laser light of different wavelengths to one or more remote satellites. If the intensity of the light is modulated with the data sequence to be transmitted, the term communication mode is used; if both satellites emit laser light to xe2x80x9cfindxe2x80x9d themselves, the term acquisition mode is used. In both modes, the respective remote satellite appears virtually point-like to the other satellite, owing to the large distances (up to 70,000 km in geostationary orbit).
In both cases, the receiving optical system has to process very low light powers. The optical systems must therefore primarily have high luminous intensity. In the case of point-like objects, the irradiation intensity b at the location of the receiver is given by
bxe2x89xa1W/A=D2xc2x7sin2(xcex4)xe2x80x83xe2x80x83(1)
where W is the incident radiant power, A is the area of the diffraction disk, D is the diameter of the entry pupil and xcex4is the opening angle of the telescope (R.W. Pohl, Einfxc3xchrung in die Physik [Introduction to Physics], Volume 3, page 64). sin(xcex4) is referred to as the numerical aperture NA of the telescope, which is derived from the F number
F#xe2x89xa1F/Dxe2x80x83xe2x80x83(2)
using the focal distance F according to the relationship
NA=1/(2*F#)xe2x80x83xe2x80x83(3)
Systems having high luminous intensity and intended for quasi-point-like objects are thus distinguished by a large diameter D or by a large numerical aperture NA or by both.
In astronomy, the approach of choosing D to be very large is adopted. The large 8 m telescopes on Mount Palomar and other astronomical centers are known. Although for reasons of technical feasibility the numerical aperture must be kept small, the gain in luminous intensity is considerable. Owing to the small numerical aperture, according to (3) the focal distance is correspondingly increased and hence also the telescope dimensions. Above a certain diameterxe2x80x94typically above 30 cmxe2x80x94it is possible only to use mirror systems since lens systems can no longer be expediently produced.
The second major advantage of reflecting mirror systems over optically refracting lens systems is their freedom from chromatic aberration. An optically corrected mirror system can thus be used both in the UV range and far into the infrared range, which is of decisive importance especially for astronomy.
On the other hand, the disadvantage of mirrors is the small field of view of only a few degrees, whereas lens systems in turn can be designed to be extremely wide-angled (cf. fisheye systems with fields of view greater than 180xc2x0). In astronomy, this disadvantage is overcome elegantly but in a very expensive manner by enormous mechanical tracking units in order to achieve a large celestial field of view.
Historicallyxe2x80x94and also as a rule also todayxe2x80x94lenses and mirrors having a spherical surface are produced; a production process developed to maturity over centuries. If it is necessary to position a plurality of spherical mirrors one behind the other, as in a telescopexe2x80x94these should have a common or optical symmetry axis (xe2x80x9con-axisxe2x80x9d arrangement). If this is not the case, the result may be deteriorations in the imaging quality. In the xe2x80x9con-axisxe2x80x9d mode, however, the problem of internal obscuration arises, leading on the one hand to losses of light and on the other handxe2x80x94often worsexe2x80x94to troublesome diffraction artefacts. Diffraction artefacts adversely affect the image quality in imaging telescopes whereas, in the case of space telescopes, they lead to an undesired beam expansion and hence to critical energy losses at the remote satellite.
However, the obscuration can be avoided if the mirrors are operated xe2x80x9coff-axisxe2x80x9d. Consequently, a normal, rotationally symmetrical xe2x80x9cparentxe2x80x9d mirror is first produced but only a generally round section thereof remote from the optical axis is used. However, this results in image deterioration, the compensation of which is also the object of the present invention.
Aspherical mirrors are more difficult to produce than spherical mirrors. For very high quality requirements, however, aspherical mirrors are indispensable. In the case of aspherical shapes, a distinction is made between xe2x80x9cconicalxe2x80x9d mirrors, such as paraboloids of revolution, ellipsoids of revolution or hyperboloids of revolution, and more complex, nonconical aspherical shapes. The degree of difficulty increases sharply in the case of the latter, particularly in the case of mirrors of large diameter and low F numbers. From F numbers of less than 2, moreover, the measurement and testing equipment has to meet very high requirements.
In satellite communication, the situation is completely different from that in astronomy. Here, primarily the telescope dimensions and the weight have to be minimized; they are essentially responsible for the high costs. A satellite telescope therefore consists predominantly of systems of smaller dimension. Mirrors are chosen since, when constructed in the highly developed lightweight construction method, they can have a significantly lower weight than optically equivalent lens systems. Lens systems are moreover very problematic for space flights since it is necessary to take expensive protective measures to prevent fogging of glass in the lenses, which is caused by the high-energy cosmic radiation.
A further advantage of mirror systems is that the volume occupied can be minimized if the mirror arrangement is xe2x80x9cnestedxe2x80x9d in an appropriately skilled manner. However, nesting is already a necessity in the xe2x80x9coff-axisxe2x80x9d systems described above, but it has even further advantages:
On the one hand, a compact arrangement makes the optical system thermally more stable. Since satellites are exposed to extreme temperature differences, the following design rule is applicable: the smaller the dimension, the smaller the defocusings of the optical system which are caused by the thermal expansion of the mechanical structure. Defocusing of only a few xcexcm can lead to unacceptable wavefront deformations.
Designers must furthermore minimize the natural vibrations of the satellite. A vibrating satellite results in a dramatic deterioration in the xe2x80x9cpointingxe2x80x9d stability of the optical connection: this is understood as meaning that, owing to the large distances, vibrations cause intensity variations at the location of the remote satellite. Intensity variations in turn influence the error rate of the data transmission (bit error rate) and must be compensated by an undesired reduction in the data rate. The vibrations are due to the lack of a mechanical fixed point in the orbit. Thus, each new orientation of the satellite must be mechanically opposed, i.e. it must be actively damped. This leads to control sequences which, particularly in the vicinity of natural frequencies of the structure, become very complicated. Here too, the following is therefore applicable: the smaller the size, the easier the stabilization. The manner in which vibrations are rated as critical is evident from the fact that the tolerance for the pointing stability is specified as typically 50 nanorad, i.e. a hundredth of an arc-second (!!).
There are two possibilities for transmitting sufficient optical power to the remote satellite, in spite of the small mirror diameter: powerful laser light sources are used and the numerical aperture NA of the telescope is increased according to (1).
A large NA is almost always necessary since, in addition to the pure communication and acquisition with well collimated laser light, many satellites also have to xe2x80x9coperatexe2x80x9d in an optically passive manner, i.e. quasi-astronomically. Thus, a satellite registers continuously selected star images according to which it orients itself in three dimensions if it has to be brought into a new position in the so-called xe2x80x9cpointingxe2x80x9d mode. For safety and cost reasons, however, the same telescope optical system is used for the communication, acquisition and xe2x80x9cpointingxe2x80x9d channel.
The following modes are thus performed by a modern space telescope:
The optical communication is effected at 1064 nm in the bidirectional xe2x80x9csend and receivexe2x80x9d mode, with a small field of view, e.g. of 0.1xc2x0, very high wavefront quality ( less than xcex/30 rms) and high data rate ( greater than 10 Gbyte/sec). The optical acquisition is performed at (800-900 nm), likewise in the bidirectional xe2x80x9csend and receivexe2x80x9d mode, with a relatively large field of view of 3xc2x0, wavefront of normal quality ( less than xcex/10 rms) and average data rate (50-100 kbyte/sec). Finally, the so-called optical xe2x80x9cpointingxe2x80x9d is performed in the passive xe2x80x9creceivexe2x80x9d mode, likewise with a large field of view of 3xc2x0 and a wavefront of normal quality ( less than xcex/10 rms) but with a broad spectral correction (500-1000 nm).
This means that mirror systems for space applications in the communication sector are of relatively small diameter (200-300 nm) and large numerical aperture. For weight and stability reasons, they must be nested in a mechanically highly complex manner. The optical quality must be very good for the communication, acquisition and xe2x80x9cpointingxe2x80x9d channel, i.e. diffraction-limited.
Such an optical system or telescope is disclosed, for example, in U.S. Pat. No. 5,309,276. The telescope is described very generally herein without the demanding requirements of practice, in particular of space flight, being taken into account.
On the one hand, the space required is relatively large since the primary mirror and the secondary mirror have a common optical axis, i.e. are not optimally folded in the context of the above design. In order, nevertheless, for a certain field of view, to guide the beam from the primary to the secondary mirror without cutting, the secondary mirror must be relatively far away from the primary mirror. As mentioned above, this is disadvantageous if large temperature variations are expected in the operating mode. Furthermore, this unnecessarily enlarges the unused central zone of the primary mirror operated xe2x80x9coff-axisxe2x80x9d, which requires a large diameter of the xe2x80x9cparentxe2x80x9d mirror. In order nevertheless to reduce the dimension of the telescope, the xe2x80x9cparentxe2x80x9d mirror was designed with an F number≈1. This can be realized in practice for the stated magnitude of the diameter only at very great expense, owing to the very narrow manufacturing tolerances. In the case of this F number, furthermore, the testing technology has to meet very high requirements.
The publication also notes that, in the case of an inadequate wavefront quality, all mirrors can be given an asphericity higher than conical. However, in the case of large mirrors, this is a more expensive and technically very uncertain variant.
Another disadvantage is that the small mirror M3 can be kept planar only with an afocal magnification xcex93=6.5. At other magnifications, it must be made concave or convex, which on the one hand further increases the costs but on the other hand also complicates the adjustment of the entire system.
If all the disadvantages are combined, the present variant proves to be a nonoptimized, inflexible, sensitive and expensive solution. It is therefore not suitable in practice in this form.
The object of the present invention is to overcome these restrictions and to permit the construction of compact, wide-angle and obscuration-free systems which have high luminous intensity and meet practical requirements. It is intended to find an optical solution which meets the abovementioned, demanding requirements, some of which are contradictory. It will be shown that this can be carried out according to the invention in a stable and economic manner by means of a single correction surface.
Accordingly, it is initially the object of the invention to provide an optical system, in particular a telescope, which is corrected in a simple manner, or a telescope which also meets practical requirements with substantially smaller dimensions, lower weight and lower costs. This is achieved in a surprisingly simple manner by the characterizing features of claims 3 and 5, respectively.
An optical system according to claim 3 even permits an optimal correction if, as in the case of space telescopes, satisfactory operation is required simultaneously in a plurality of optical channels. As mentioned above, the optical requirements of communication differ from those for acquisition and for xe2x80x9cpointingxe2x80x9d. Nevertheless, it is easily possible in the manner according to the invention simultaneously to perform a correction by means of a single correction surface, which to date has been possible only by making compromises.
As is evident from the defining clause of claim 6, one object of the invention is first achieved by accepting an optical error, which however is eliminated again by the measure stated in the defining clause of claim 5, so that in the end only the advantages of the first measure remain. In addition, an initially unexpected additional effect has resulted, namely that the third reflector can be kept planar also in the case of afocal magnifications which are greater than 6.5. Of course, this makes a significant contribution to cost reduction and to simplification of production.
The method developed for producing a correction in such a telescope is expediently that according to claims 1 and 2, and it has been foundxe2x80x94quite independently of the optical system to which it is appliedxe2x80x94that a number of errors which adversely affect the wavefront can in principle also be eliminated therewith. Thus, residual aberration errors of the design, caused by the shape, position and tilting of the off-axis aspherical shapes, can be eliminated. Furthermore, it is possible and also required in practice, to compensate residual polishing and assembly errors of the optical components. The correction measure is derived from the measured values, and it is for this reason that the invention also relates generally to an optical system as claimed in claims 3 and 4.
It has been found that tilting of the first reflector by the angle stated in claim 7 is capable of keeping the asymmetry error within controllable limits, which is why such a tilt is preferred. It is in turn surprising that only a relatively small tilt of, for example, 1xc2x0, at which the asymmetry error is very small, is capable of delivering the advantages mentioned at the outset, and it is therefore certainly no small merit of the present invention to have recognized this. A tilt of only, for example, 30 arc-seconds can result in a substantial improvement.
According to claim 4, the correction is preferably made on the third reflector, because this will in general be smaller than that of the first and the fourth reflector and optically also less sensitive, and is close to the intermediate focal plane and not too far away from the plane of the pupil. It can thus be used both for correcting focal plane errors and for correcting pupil errors. In addition, the third reflector in an embodiment according to the invention may be planar.
The manner in which an asymmetry error is eliminated in practice is per se within the capabilities of an average skilled worker in the area. However, a procedure according to claim 4 involving a polynomial formulation is preferred.
A criticism above of the prior art was that the xe2x80x9cparentxe2x80x9d mirrors have an F number of 1. In the invention, the measures according to claims 5 and/or 6 can be particularly easily realized.
To limit the asymmetry error, it is advantageous if the features of claim 7 are realized.
For this purposexe2x80x94for example for a telescope according to the invention, the first, second and fourth reflectors are calculated so that their xe2x80x9cparentxe2x80x9d mirrors do not fall below the F number of 1.5, which is still acceptable in terms of manufacture.
Reflectors operated xe2x80x9coff-axisxe2x80x9d (the first, second and fourth reflectors) are tilted relative to one another. On the one hand, this results in a compact assembled volume and, on the other hand, the wavefront errors introduced by the xe2x80x9coff-axisxe2x80x9d mode can already be partially compensated.
The remaining errors are corrected by the aspherical shape of the mirror surfaces. Once again for reasons of greater feasibility, the three large mirror reflectors (the first, second and fourth reflectors) are designed as purely conical mirrors, while the third reflector is designed as a pure plane mirror. For reasons of flexibility, this should be applicable for a large afocal magnification range xcex93=4-15. The plane mirror (the third reflector) can, according to the invention, have a reflecting phase plate which possesses a structured surface and with which the final fine correction of the optical wavefront is achieved. The phase plate can also be introduced as a transmitting glass plate close to the third reflector.
The production of such a structured plate is permitted by new technical possibilities for mechanical surface processing in order to polish and to measure mirror surfaces having any desired depth profile in optical quality.
However, it can also be designed as a diffracting element in the form of a hologram. The hologram can then be cemented to the planar surface of the third reflector element.
Providing additional degrees of freedom of the mutual tilting and of the phase correction plate, it is possible to find, for a large range of the afocal magnification, solutions which significantly improve the wavefront quality. All these solutions fulfil the technically important general condition that the exit pupil AP is mechanically accessible outside the telescope.